Deformations of asymptotically cylindrical G2-manifolds

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Abstract

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G2-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G2-manifold is exactly G2 if and only if the fundamental group π1(M) is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

Original languageEnglish
Pages (from-to)311-348
Number of pages38
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume145
Issue number2
Early online date19 May 2008
DOIs
Publication statusPublished - 1 Sep 2008

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